In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists. In mathematical logic, this sort of quantification is known as uniqueness quantification or unique existential quantification. Uniqueness quantification is often denoted with the symbols "∃!" or ∃=1". For example, the formal statement may be read aloud as "there is exactly one natural number n such that n - 2 = 4". Reduction to ordinary existential and universal quantification Uniqueness quantification can be expressed in terms of the existential and universal quantifiers of predicate logic by defining the formula ∃!x P(x) to mean . An equivalent definition that has the virtue of separating the notions of existence and uniqueness into two clauses, at the expense of brevity, is . Another equivalent definition with the advantage of brevity is . Generalizations One generalization of uniqueness quantification is counting quantification. This includes both quantification of the form "exactly k objects exist such that ..." as well as "infinitely many objects exist such that ..." and "only finitely many object exist such that...". The first of these forms is expressible using ordinary quantifiers, but the latter two cannot be expressed in ordinary first-order logic. Retrieved from "http://en.wikipedia.org/wiki/Uniqueness_quantification" Categories: Quantification | One | Mathematical terminology Views Article Discussion Edit this page History Personal tools Log in / create account if (window.isMSIE55) fixalpha(); Navigation Main page Contents Featured content Current events Random article Search   Interaction About Wikipedia Community portal Recent changes Contact Wikipedia Donate to Wikipedia Help Toolbox What links here Related changes Upload file Special pages Printable version Permanent linkCite this page Languages Français Nederlands Türkçe 中文 This page was last modified on 4 February 2009, at 21:24. All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.) Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a U.S. registered 501(c)(3) tax-deductible nonprofit charity. Privacy policy About Wikipedia Disclaimers if (window.runOnloadHook) runOnloadHook();

Sex toys | Crazy XXX Videos | Nudist Pics | LoveKiller | HomeMadeFucked | MyPersonalFriends | Timekiller Erotic | add hardlink